Solución

a.      y=rcosθ,z=rsenθ,x=z\text{a.}\;\;\;y = rcos\theta, z = rsen\theta, x = z E={(r,θ,z)1r3,0θ2π,0z1r2},f(r,θ,z)=zE = \lbrace (r, \theta, z)|1 \le r \le 3, 0 \le \theta \le 2\pi, 0 \le z \le 1 - r^2\rbrace, f(r, \theta, z) = z b.      1302π01r2f(r,θ,z)zrdzdθdr=356π3\text{b.}\;\;\;\int_1^3\int_0^{2\pi}\int_0^{1-r^2} f(r, \theta, z)zrdzd\theta dr = \frac{356\pi}{3}